anonymous
  • anonymous
Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..
OCW Scholar - Single Variable Calculus
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
A "differentiable function" is one which is continuous over all the values of x you're interested in, and its derivative is also continuous. This means there are no sharp corners in the original function, only smooth transitions.
anonymous
  • anonymous
Differentiation is defined by a limit, and limits need not always exist. If the limit \[\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\] exists at a particular x value then we say the function is differentiable at that point. It it exists for all x in an interval then it is differentiable on that interval. Note that the limit is double sided, so implicit in this definition is the fact that no function defined on a closed interval can be differentiable on that closed interval, thus why the wording of many of the basic theorems insist on certain intervals being open...

Looking for something else?

Not the answer you are looking for? Search for more explanations.